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Finding the Third Proportional to 6,506 and 14,278

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Solution

The third proportional to 6,506 and 14,278 is: 31,334.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,506 : 14,278 = 14,278 : x
  2. Step 2: Convert to fraction form
    6,506/14,278 = 14,278/x
  3. Step 3: Cross multiply
    6,506x = 14,278 × 14,278
  4. Step 4: Simplify right side
    6,506x = 203,861,284
  5. Step 5: Solve for x
    x = 203,861,284/6,506
  6. Step 6: Final answer
    x = 31,334.35

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.